It's already been mentioned by /u/DeSoulis that we don't know. No one's been found (that the public knows of) who's been shown to be him. I just want to expand on that answer a little more.

Not being able to find/identify him wasn't for lack of trying. Obviously it was something people were trying to do from the time it happened. There was some speculation of who it might have been, but official records show that they were never able to find him.

It was reported shortly after it happened that the person was a teenager named Wang Weilin, however the official records are that no person by that name was among those imprisoned or dead.

Jiang Zemin, speaking to ABC News and then quoted in the 1990 LA Times article (where he was first identified to Americans, despite the name originally coming from the Daily Express), echoed this. Quoting here from the times article:

Communist Party chief Jiang Zemin said in a May 2 interview with ABC Television that the dramatic pictures illustrated the army's restraint.

He said the pictures showed tank drivers would not run down a citizen and proved the allegations of tanks crushing demonstrators were lies.

Jiang said he could not confirm whether the man was arrested. When asked whether the young man had been executed, Jiang replied in English: "I think never, never killed."

The problem is now just how much you want to believe the official Party line. It's just as likely that he was tracked down immediately as it is that he disappeared and kept his mouth shut, and we aren't likely to ever know either way.

I know Wikipedia isn't really worthwhile for most stuff but it's interesting to see how the Mandarin article on Wang (which is named for the person and not called something like "Tank Man", 坦克人) puts it:

但儘管「王維林」是當前絕大部份中文媒體對於該名男子的稱呼，然而這個名字最早是以英文「Wang Weilin」出現在英國的《 星期日快報 》上 ，實際上到了今日有關該人物的真實姓名、身分以及下落仍然沒有獲得確認。

Despite being named as "Wang Weilin", and despite this being the name he has been known as in [Chinese] media, this name is actually coming from the English name "Wang Weilin", published in the British paper "Daily Express". The mans actual identity and whereabouts are still unknown.

Point being, there's a huge amount of speculation of who he is/was, both in China and out, but nothing conclusive has ever come up.

The answer is that nobody knows what happened to him and it's very doubtful if anyone will ever know, nobody was even able to identify who he is that we know of. He could have being arrested/killed by the government, or he could have decided to simply lay low for the rest of his life.